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4 years ago

MATH HELP

Mathematics

2 answers:

Veronika [31]4 years ago

4 0

The remaining area is 20% of the previous area.

Hope this Helps!

LenKa [72]4 years ago

4 0

Let's just take a look at the first two points plotted, (0,100) and (1, 80). The difference between 100 and 80 is 20, but what percent of 100 is 20? Well, since any percent x% can be represented as a fraction in the form $\frac{x}{100}$ , and the the ratio of 20 to 100 is already $\frac{20}{100}$ , our answer is a 20% decrease, which means that you're taking 100 - 20 = 80% of the previous area at each point.

Edit: Since I misread the question, I want to reframe my previous explanation instead in terms of what percent of the area of the previous point is left.

Looking again at the areas plotted, what percent of 100 sq. cm is 80 sq. cm? We want to translate the question into math, and our first indicator of where to start is the phrase "what percent of 100 sq. cm." When we talk about taking a fraction or percent of another quantity, we're usually referring to multiplying that fraction by that quantity. In this case, we have our unknown percent, $\frac{x}{100}$ , multiplied by 100, which, of course, just leaves you with x. And we're told that this quantity is equal to 80, so we have our answer. x = 80, so we're going to be taking 80% of the area each step.

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An industrial expert claims that the average useful lifetime of a typical car transimssion which comes with ten years warranty i

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Answer:

a. none of these answers

Data provides sufficient evidence, at 1% significance level, to support the expert's claim. In addition the p-value (or the observed significance level) is equal to P( T >3.281)

Step-by-step explanation:

Data given and notation

$\bar X=13.5$ represent the mean height for the sample

$s=3.2$ represent the sample standard deviation for the sample

$n=9$ sample size

$\mu_o =10$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 10 years, the system of hypothesis would be:

Null hypothesis: $\mu \leq 10$

Alternative hypothesis: $\mu > 10$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{13.5-10}{\frac{3.2}{\sqrt{9}}}=3.28$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=9-1=8$

Since is a one side right tailed test the p value would be:

$p_v =P(t_{(8)}>3.281)=0.00558$

Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can't conclude that we have a mean higher than 10 years at 1% of significance.